LAGUARDIA COMMUNITY COLLEGE
CITY UNIVERSITY OF NEW YORK
DEPARTMENT OF MATHEMATICS, ENGINEERING AND COMPUTER SCIENCE
MAT 117 – ALGEBRA AND TRIGONOMETRY
6 Lecture Hours, 1 Lab Hour, 3 Credits
Prerequisite: MAT095 or placement (If you do not have the prerequisite, you may be removed from the
course without notice.)
CATALOG DESCRIPTION
MAT117 comprises topics from both elementary and intermediate algebra and enables students requiring
remedial MAT096 to earn college credit for MAT115 at the same time. All intermediate algebra topics
are treated--polynomial, rational, exponential, logarithmic, and trigonometric expressions/functions in
addition to basic right-triangle trigonometry. Rates of change and mathematical modeling are featured
when appropriate. Instructional methods include lecture, guided groupwork and instructor feedback.
PURPOSES AND GOALS
MAT117 is designed to allow students who require MAT096 and college algebra to exit developmental
mathematics and earn college credit within one semester. There will be strong emphasis on the conceptual
aspects of algebra that underlie algebraic procedures. Because research shows that pedagogy is as
important as curriculum for student success, instructors will employ a variety of instructional methods
(e.g., lecture, guided groupwork, and graded/nongraded formative assessments/feedback).
INSTRUCTIONAL OBJECTIVES
1. Enable students to improve their accuracy and fluency with the four fundamental arithmetic
operations.
2. Introduce students to the concept of function and its application in modeling (linear and exponential
cases in particular).
3. Familiarize students with the equivalence between the rate of change of a linear function and the
(constant) slope of its graph, enabling students to graph straight line equations.
4. Introduce students to quadratic functions and their graphs, and enable them to find "zeroes" by
solving quadratic equations.
5. Familiarize students with the arithmetic of rational expressions, reinforce the algebra required to
solve equations involving rational expressions, and introduce rational functions.
6. Familiarize students with the arithmetic of radical expressions and provide them with algebraic
methods for solving equations involving radicals.
7. Introduce students to exponential and (via the concept of inverse) logarithmic functions, and their
graphs; additionally, provide students with the requisite computational and algebraic skills necessary
to solve exponential and logarithmic equations.
8. Introduce students to right-triangle trigonometry, featuring the basic trigonometric ratios; and then
familiarize them with the properties of the sine and cosine functions.
PERFORMANCE OBJECTIVES
1. Add, subtract, multiply, and divide rational and decimal numbers with accuracy and fluency.
2. Explain and describe the functional concept/properties, and compare and contrast linear and
exponential data.
3. Describe the equivalence of rate of change and slope for a linear function, and apply it in graphing
straight lines.
4. Graph quadratic functions and solve quadratic equations.
5. Carry out arithmetic operations with rational expressions and solve equations involving them.
1|Page
MAT 117 s yllabus Spring 2015
6. Carry out arithmetic operations with radical expressions and solve equations involving them.
7. Sketch graphs of exponential and logarithmic functions, and solve exponential and logarithmic
equations.
8. Solve right-triangle trigonometry problems and sketch the graphs of the sine and cosine functions.
Required Textbook: College Algebra (Special Edition for LaGuardia Community College) by Julie
Miller, McGraw-Hill, 2015.
Required Online Access: www.aleks.com. New copies of the required textbook contain an online access
code.
Evaluation:
The purpose of a grading system is to give students, and those who will read their transcripts, an accurate
record of their performance in this course. The role of the Mathematics, Engineering and Computer
Science Department is to provide a fair, valid, and reliable structure for assessing student achievement.
CATEGORY
Online (Pie) Homework
Quizzes
Projects
Instructor’s Tests
Departmental Final Exam
PERCENTAGE
10%
5%
10%
45%
30%
EXPLANATION OF GRADING CATEGORIES
Online (Pie) Homework: Students will work online on an “ALEKS pie” containing 12 course objectives.
Each objective includes numerous topics. Credit will be earned for each mastered topic.
Quizzes: Several short assessments will be administered throughout the semester.
Projects: Your instructor will assign inquiry-learning projects throughout the semester (examples may be
found at http://ctl.laguardia.edu/pql/sampler/).
Instructor’s Tests: Your instructor will develop and administer three tests during the course of the
semester.
Departmental Final Exam: This two-hour written exam will be given during final examination week. It
will be cumulative and cover all topics.
PASSING GRADE POLICY
In order to pass this course, you must have an average total score of at least 60% and no more than 12
hours of unexcused absences.
ACADEMIC INTEGRITY
This class will be conducted in compliance with LaGuardia Community College’s academic integrity
policy.
ATTENDANCE
The maximum number of absences will be 12 hours. Unexcused absences beyond this maximum will
result in a grade of WU or F.
2|Page
MAT 117 s yllabus Spring 2015
COURSE OUTLINE
Week
Lesson
1-2
3
Week 1
4
5
6
7
8-9
Week 2
10
11
12-13
Week 3
14
15
16-21
Week 4
Opposite and Absolute Value,
Arithmetic of Real Numbers (P.788)
Area and Perimeter of Basic Figures
and Compositions Thereof
Inequalities and the Number Line –
Interval and Set-Builder Notation (P.9)
Positive Integer Exponents, Square and
Cube Roots
Order of Operations
Algebraic Expressions, Simplifying,
and Evaluating (P.24)
Properties of Exponents (P.35)
Scientific Notation
Rational Exponents (P.49)
Simplifying Radical Expressions
(Square Root Only)
Polynomials
Polynomial Addition and Subtraction
(P.63)
Multiplication of Polynomials and
Special Products
Factoring Polynomials (P.76)
23-24
Rational Expressions, Simplifying and
Multiplying (P.88)
Adding and Subtracting Rational
Expressions
25
Rationalizing the Denominator (Square
Root Only)
26
Exam 1
22
3|Page
Topic
Section
(Exercises)
A2*(11-52)
(P.799)
Supplemental
Materials
R.1(41-72)
(P.21)
R.1(93-102)
(P.22)
R.1(103-116)
(P.22)
R.45-50
(P.32),
69-90 (P.33),
91-96) (P.33)
R.3(13-70)
(P.44)
R.3(71-98)
(P.45)
R.4(27-54)
(P.59)
R.4(67-70(a)
(P.60),
75-78, 83-84)
R.5(15-22)
(P.71)
R.5(23-28)
R.5(29-54)
R.6(13-56,61)
(P.85)
R.7(15-42)
(P.99)
R.7(43-54)
(P.100)
R.7(71-72,
79-86)
(P.101)
MAT 117 s yllabus Spring 2015
Pie Homework
Arithmetic
Review
Exponents/
Scientific Notn
Radicals/
Ratl. Exponents
Polynomials &
Factoring
Rational
Expressions
27-28
29
Week 5
30
31
32
33-34
35
36
Linear Equations (P.115)
Similar Triangles
Rational Equations that Simplify to
Linear
Markups and Markdowns
Literal Equations
Solving Quadratic Equations –
Factoring and Quadratic Formula
(P.151)
Applications of Quadratic Equations
(P.166)
Rational Equations that Simplify to
Quadratic (P.176)
Radical Equations (Square Root Only)
37
Linear Inequalities (P.187)
Week 6
38
39
Absolute Value Equations
Absolute Value Inequalities (P.198)
40
The Cartesian Coordinate System
(P.219)
The Pythagorean Theorem
41
Week 7
42
4|Page
43
44
Distance in the Cartesian Coordinate
System
Functions and Relations
Function Notation (P.239)
Intercepts of Functions
Domain and Range
Interpreting the Graph of a Function
1.1(15-48)
(P.124)
Supplemental
Materials
1.1(49-69)
(P.126)
Supplemental
Materials
1.1(69-90)
(P.126)
1.4(15-34,
57-96)
(P.161)
1.5(5-10,
33-38)
(P.172)
1.6(19-26)
(P.184)
Linear
Equations
Quadratic &
Radical Eqns.
1.6(31-34,
39-42)
(P.185)
1.7(13-30,
49-54)
(P.194)
1.8(13-32)
1.8(33-56)
(P.203)
2.1(9-10)
(P.226)
Supplemental
Materials
2.1(11-18(a))
(P.226)
2.3(15-18,
21-38)
2.3(41-59)
(P.248)
2.3(73-74)
2.3(85-108)
(P.250)
2.3(109-112)
(P.251)
MAT 117 s yllabus Spring 2015
Inequalities &
Functions
45
46-48
Linear Functions – Graphing by Point
Plotting (P.253)
2.4(19-30)
(P.264)
Slopes, intercepts, graphs, and
equations of lines
2.4(35-50,
59-70,73-86)
(P.265)
Linear Models (P.270)
2.5(57-68)
(P.281)
Properties and Graphs of Square and
Cube Root Functions
Supplemental
Materials
49
50
Exam 2
Week 8
51
52-53
54
Quadratic Functions and their Graphs
(P.351)
Week 9
57-58
59-60
61-62
3.1(31-44)
Division of Polynomials (P.380)
3.3(17-30)
(P.389)
Rational Functions – Domain and
Vertical Asymptotes (P.410)
3.5(17-34)
(P.426)
Week 10
65-66
67
68-69
5|Page
Root,Qdratic,&
Ratl Fctns
Exponential Functions and their Graphs 4.2(19-48)
(Graph by Point Plotting Only) (P.484) (P.493)
Exponential models
Logarithmic functions and their graphs
(P.499)
Properties of Logarithms (P.515)
63-64
3.1(23-30)
(P.360)
Quadratic Models
55
56
Linear
Functions
4.2(55-67)
(P.494)
4.3(19-54,
57-92)
(P.509)
4.4(17-68)
(P.522)
Exponential and Logarithmic Equations 4.5(11-37,
(P.525)
41-62)
(P.535)
Exponential Models Continued
4.5(63-68)
(P.535)
4.6(23-38)
(P.548)
Systems of Linear Equations (P.567)
5.1(7-48)
(P.575)
MAT 117 s yllabus Spring 2015
Exps,Logs,&Linear
Systems
Angles and their Measurement (P.652)
70-71
Week 11
Right triangle trigonometry (P.670)
72-73
74
Applications of Right Triangle
Trigonometry
Exam 3
75
Week 12
76-79
80-81
82-83
84
A1**.1(25-26,
35-56)
(P.663)
A1.2(13-32
(P.683),
(61-64)
(P.685)
A1.2(65-73)
Trigonometric functions of any angle
(P.688)
A1.3(15-21,
23-54, 63-68)
(P.697)
Graphs of Sinusoidal Functions (no
A1.5(9-12,
Phase Shift) (P.718)
15-16, 19-34)
(P.730)
Sinusoidal Modeling (no Phase Shift)
A1.5
(35-36,74)
(P.731)
Preparation for the final exam
*
Appendix 2: Operations on Real Numbers
Appendix 1: Trigonometry
**
6|Page
MAT 117 s yllabus Spring 2015
Trigonometry